Research

 
 Publications: 

• Desingularization and global continuation for hollow vortices, with S. Walsh and M. Wheeler, submitted.

• Global bifurcation for monotone fronts of elliptic equations, with S. Walsh and M. Wheeler, J. Eur. Math. Soc., to appear.

• On the inviscid limit of the compressible Navier-Stokes equations near Onsager's regularity in bounded domains, with Z. Liang, D. Wang and R. Xu, SCIENCE CHINA Mathematics, to appear.

• Rigidity of three-dimensional internal waves with constant vorticity, with L. Fan, S. Walsh and M. Wheeler, J. Math. Fluid Mech., 25 (2023), no. 3, 71. PDF.

• Stabilization effect of elasticity on three-dimensional compressible vortex sheets, with F. Huang, D. Wang and D. Yuan, J. Math. Pures Appl., 172 (2023), 105 – 138. PDF.

• Stability of peaked solitary waves for a class of cubic quasilinear shallow-water equation, with H. Di and Y. Liu, Int. Math. Res. Not., (2023), 6186 – 6218. PDF.

• On the vortex sheets of compressible flows, with F. Huang, D. Wang and D. Yuan, Commun. Appl. Math. Comput., (2022), 1 – 20.

• A Kato-type criterion for vanishing viscosity near the Onsager's critical regularity, with Z. Liang and D. Wang, Arch. Ration. Mech. Anal., 246 (2022), 535 – 559. PDF.

• Orbital stability of internal waves, with S. Walsh, Comm. Math. Phys., 391 (2022), 1091 – 1141. PDF.

• Center manifolds without a phase space for quasilinear problems in elasticity, biology, and hydrodynamics, with S. Walsh and M. Wheeler, Nonlinearity, 35 (2022), 1927 – 1985. PDF.

• The shallow-water models with cubic nonlinearity, with T. Hu and Y. Liu, J. Math. Fluid Mech., 24 (2022), Paper No. 59, 31pp. PDF.

• Global bifurcation of solitary waves to the Boussinesq abcd system, with J. Jin, J. Differential Equations,, 310 (2022), 235 – 263. PDF.

• Global ill-posedness for a dense set of initial data to the isentropic system of gas dynamics, with A. Vassuer and C. Yu, Adv. Math., 393 (2021), Paper No. 108507, 46pp. PDF.

• On the stability of two-dimensional non-isentropic elastic vortex sheets, with F. Huang, D. Wang and D. Yuan, Commun. Pure Appl. Anal., 20 (2021), 2159 –. PDF.

• Transverse instability of the CH-KP-I equation, with J. Jin, Ann. Appl. Math, 37 (2021), 337 – 362. PDF.

• A rigidity property for the Novikov equation and the asymptotic stability of peakons, with W. Lian, D. Wang and R. Xu, Arch. Ration. Mech. Anal., 241 (2021), 497 – 533. PDF.

• $W^{1,\infty}$ instability of $H^1$-stable peakons in the Novikov equation, with D. Pelinovsky, Dyn. Partial Differ. Equ., 18 (2021), 173 – 197. PDF.

• Global bifurcation of anti-plane shear fronts, with S. Walsh and M. Wheeler, J. Nonlinear Sci., 31 (2021), no. 2, 28. PDF.

• Large-amplitude internal fronts in two-fluid systems, with S. Walsh and M. Wheeler, Comptes Rendus. Mathematique, 358 (2020) 1073 – 1083. PDF.

• Nonlinear stability and existence of compressible vortex sheets in 2D elastodynamics, with J. Hu, D. Wang, T. Wang and D. Yuan, J. Differential Equations, 269 (2020), 6899 – 6940. PDF.

• Energy equality in compressible fluids with physical boundaries, with Z. Liang, D. Wang and R. Xu, SIAM J. Math. Anal., 52 (2020), 1363 – 1385. PDF.

• Linear stability of compressible vortex sheets in 2D elastodynamics: variable coefficients, with J. Hu and D. Wang, Math Ann., 376 (2020) 863 – 912. PDF.

• Existence, nonexistence, and asymptotics of deep water solitary waves with localized vorticity, with S. Walsh and M. Wheeler, Arch. Ration. Mech. Anal., 234 (2019) 595 – 633. PDF.

• Onsager's energy conservation for inhomogeneous Euler equations, with C. Yu, J. Math. Pures Appl., 131 (2019) 1 – 16. PDF.

• Analysis of variable-step/non-autonomous artificial compression methods, with W. Layton and M. Mclaughlin, J. Math. Fluid Mech., 21 (2019) Art. 30, 20 pp. PDF.

• Martingale solutions for the three-dimensional stochastic nonhomogeneous incompressible Navier-Stokes equaitons driven by Levy processes, with D. Wang and H. Wang, J. Funct. Anal., 276 (2019) 2007 – 2051. PDF.

• Existence and uniqueness of global conservative weak solutions for the integrable Novikov equation, with G. Chen and Y. Liu, Indiana U. J. Math, 67 (2018) 2393 – 2433. PDF.

• On a shallow-water approximation to the Green-Naghdi equations with the Coriolis effect, with G. Gui and Y. Liu, Adv. Math., 340 (2018) 106 – 137. PDF

• Lipschitz metric for the Novikov equation, with H. Cai, G, Chen and Y. Shen, Arch. Ration. Mech. Anal., 229 (2018) 1091-1137. PDF

• Existence and qualitative theory for stratified solitary water waves, with S. Walsh and M. Wheeler, Ann. Inst. H. Poincare Anal. Non Linearie, 35 (2018) 517-576. PDF

• Reconstruction of stratified steady water waves from pressure readings on the ocean bed, with S. Walsh, J. Differential Equations, 264 (2018) 115-133. PDF

• Breaking waves and solitary waves to the rotation-two-component Camassa-Holm system, with L. Fan, H. Gao and Y. Liu, SIAM J. Math. Anal., 49 (2017) 3573-3602. PDF

• Linear stability of compressible vortex sheets in two-dimensional elastodynamics, with J. Hu and D. Wang, Adv. Math., 311 (2017) 18-60. PDF

• Pressure transfer functions for interfacial fluid problems, with V. Hur and S. Walsh, J. Math. Fluid Mech., 19 (2017) 59-76. PDF

• On the existence and qualitative theory of stratified solitary water waves, with S. Walsh and M. Wheeler, C. R. Math. Acad. Sci. Paris, 354 (2016) 601-605. PDF

• Global weak solutions to the inhomogeneous MHD-Vlasov equations, with J. Hu and D. Wang, J. Math. Fluid Mech., 18 (2016) 343-360. PDF

• Analysis on the blow-up solutions to a class of integrable peakon equations, with F. Guo, Y. Liu and C.-Z. Qu, J. Funct. Anal., 270 (2016) 2343-2374. PDF

• Stability of the Camassa-Holm peakons in the dynamics of a shallow-water-type system, with X. Liu, Y. Liu and C.-Z. Qu, Calc. Var. Partial Differ. Equ., 55 (2016) 55:34. PDF

• A nonlinear parabolic equation with discontinuity in the highest order and applications, with Q. Liu, J. Differential Equations 260 (2016) 1200-1227. PDF

• Continuous dependence on the density for stratified steady water waves, with S. Walsh, Arch. Ration. Mech. Anal. 219 (2016) 741-792. PDF

• Oscillation-induced blow-up to the modified Camassa-Holm equation with linear dispersion, with Y. Liu, C.-Z. Qu and S.-H. Zhang, Adv. Math. 272 (2015) 225-251. PDF

• Existence and symmetry of ground states to a Boussinesq abcd system, with E. Bao and Q. Liu, Arch. Ration. Mech. Anal. 216 (2015) 569-591. PDF

• Long time existence of classical solutions to a 1-D swelling gel, with M.C. Calderer, Math. Mod. Meth. Appl. S. 25 (2015) 165-194. PDF

• The Holder continuity of the solution map to the b-family equation in weak topology, with Y. Liu and P.-Z. Zhang, Math Ann. 357 (2013) 1245-1289. PDF

• On the ill-posedness of a weakly dispersive one-dimensional Boussinesq system, with Y. Liu, J. Anal. Math. 121 (2013) 299-316. PDF

• Stability of the mu-Camassa-Holm peakons, with J. Lenells and Y. Liu, J. Nonlinear Sci. 267 (2013) 97-112. PDF

• On the regularity of the flow map of the gravity-capillary equations, with J. L. Marzuola, D. Spirn and J. D. Wright, J. Funct. Anal. 264 (2013) 752-782 PDF

• Asymptotic behavior and symmetry of condensate solutions in electroweak theory, with Y.-J. Guo and D. Spirn, J. Anal. Math. 117 (2012) 47-85. PDF

• Local regularity and decay estimates of solitary waves for the RMKP equation, with Y. Liu and P.-Z. Zhang, Trans. Amer. Math. Soc. 364 (2012) 3395-3425. PDF

• Stability of solitary waves of a generalized two-component Camassa-Holm system, with Y. Liu and Z. Qiao, Comm. Partial Differential Equations.(2011) 2162-2188. PDF

• Wave-breaking and global existence for a generalized two-component Camassa-Holm system, with Y. Liu, Int. Math. Res. Not. (2011) 1381-1416. PDF

• Electrically and magnetically charged vortices in the Chern-Simons-Higgs theory, with Y.-J. Guo, D. Spirn and Y. Yang, Proc. R. Soc. Lond. Ser. A 465 (2009) 3489-3516. PDF

• Symmetric planar Chern-Simons-Higgs vortices, with D. Spirn, Comm. Math. Phys., 285 (2009) 1005-1031.  PDF

• Solitary waves of the rotation-modified Kadomtsev-Petviashvili equation, with V. Hur and Y. Liu, Nonlinearity, 21 (2008) 2949-2979.  PDF

• The Cauchy problem and the stability of solitary waves of a hyperelastic dispersive equation,  Indiana U. J. Math,  57 (2008) 2377-2422.  PDF

• Some nonlinear dispersive waves arising in compressible hyperelastic plates, Internat. J. Engrg. Sci,  44 (2006) 1188-1204.  PDF

• Analysis of some nonlinear dispersive waves in a compressible hyperelastic plate, Thesis at Brown University.